Timmy consumes two commodities x and y. His utility function is min{x+ 2y, y + 2x}. He chooses to buy 10 units of good x and 20 units of good y. The price of good x is $1. What is Timmy’s income? Explain your answer.
To find Timmy's income, we need to evaluate the cost of the goods he purchased and their corresponding prices.
The cost of the 10 units of good x is given by:
10 units * $1/unit = $10
The cost of the 20 units of good y is not provided, but we can calculate it by comparing the prices of x and y using Timmy's utility function:
min{x + 2y, y + 2x}
By substituting the quantities purchased by Timmy into the utility function, we get:
min{10 + 2(20), 20 + 2(10)}
min{10 + 40, 20 + 20}
min{50, 40} = 40
Thus, the cost of the 20 units of good y is $40.
To find Timmy's income, we add up the costs of the goods he purchased:
$10 + $40 = $50
Therefore, Timmy's income is $50.